Subject:
Higher Education, Mathematics, Calculus, Geometry, Physics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
  • Algebra of Vectors
  • Component Form
  • Direction
  • Magnitude
  • Mathematics
  • Tmm0022
  • Trigonometric Form
  • Unit Vector
  • License:
    Creative Commons Attribution Non-Commercial
    Language:
    English
    Media Formats:
    Text/HTML

    Vectors in 2D

    Overview

    Vectors - magnitude, direction, component form, trigonometric form, unit vector, algebra of vectors, applications,

    TMM 002 PRECALCULUS (Revised March 21, 2017)

    AdditionalOptional Learning Outcomes:

    2. Geometry: The successful Precalculus student can:

    2e. Interpret the result of vector computations geometrically and within the confines of a particular applied context (e.g., forces).
    Sample Tasks:

    • The student can define vectors, their arithmetic, their representation, and interpretations.
    • The student can decompose vectors into normal and parallel components.
    • The student can interpret the result of a vector computation as a change in location in the plane or as the net force acting on an object.

    Vectors

    We will learn about two-dimensional vectors which are quantities that have both magnitude and direction.

    Learning Objectives:

    • Definition of a vector and its component form
    • Equality of two vectors
    • Vector arithmetic and properties
      • Vector Addition
      • Scalar Multiplication
    • Magnitude and direction of a vector, and their properties
    • Unit vector
    • Principal unit vector in the direction of positive x and y axes
    • Writing a vector in different forms
      • component form
      • principal unit vector form
      • magnitude and cosine and sine functions
    • Application to equilibrium of forces acting on a body